Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same?

HELP PLEASE!!

seropon [69]

Answer:

BD = 1 unit

AD = 1 unit

AB = 1.6 units

AC = 1.6 units

Step-by-step explanation:

In the picture attached, the triangle ABC is shown.

Given that triangle ABC is isosceles, then ∠B = ∠C

∠A + ∠B + ∠C = 180°

36° + 2∠B = 180°

∠B = (180° - 36°)/2

∠B = ∠C = 72°

From Law of Sines:

sin(∠A)/BC = sin(∠B)/AC = sin(∠C)/AB

(Remember that BC is 1 unit long)

AB = AC = sin(72°)/sin(36°) = 1.6

In triangle ABD, ∠B = 72°/2 = 36°, then:

∠A + ∠B + ∠D = 180°

36° + 36° + ∠D = 180°

∠D = 180° - 36° - 36° = 108°

From Law of Sines:

sin(∠A)/BD = sin(∠B)/AD = sin(∠D)/AB

(now ∠A = ∠B)

BD = AD = sin(∠A)*AB/sin(∠D)

BD = AD = sin(36°)*1.6/sin(108°) = 1

3 0

3 years ago

A shipment of 8 tons of sugar is separated into containers of equal size. If the shipment fills 3 1/3 containers, how much sugar

liubo4ka [24]

Take 8 and divide it by 3 1/3. to make it easer 1/3 could be .3 as a decimal.
so 8 divided by 3.3.
8/3.3= 2.42
so it would be 2.42 tons of sugar per container.

3 0

3 years ago

The rule for calculating the mean is to add up all the scores in a sample and divide by the _________

Tems11 [23]

Amount of numbers in the sample.

8 0

4 years ago

Write the equation of the parabola in vertex form.

stellarik [79]

well, looking at the picture of this vertically opening parabola, it has a vertex at 0,0 and it passes through 2,1 hmm ok

$~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y = a(x-0)^2+0\qquad \stackrel{\textit{we also know that}}{x=2\qquad y = 1}\qquad \implies 1=a(2-0)^2+0 \\\\\\ 1=4a\implies \cfrac{1}{4}=a~\hspace{10em} \boxed{y=\cfrac{1}{4}x^2}$

8 0

3 years ago

Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

EleoNora [17]

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

6 0

3 years ago

Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the​ same?

Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same?